Hamiltonian Dynamical Systems and Applications

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Craig, Walter (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Dordrecht : Springer Netherlands, 2008.
• Σειρά: NATO Science for Peace and Security Series,
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Differential equations.; Partial differential equations.; Physics.; Mechanics.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.; Ordinary Differential Equations.; Mathematical Methods in Physics.

Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical s...

Πίνακας περιεχομένων:

• Some aspects of finite-dimensional Hamiltonian dynamics
• Four lectures on the N-body problem
• Averaging method and adiabatic invariants
• Transformation theory of Hamiltonian PDE and the problem of water waves
• Three theorems on perturbed KdV
• Groups and topology in the Euler hydrodynamics and KdV
• Infinite dimensional dynamical systems and the Navier–Stokes equation
• Hamiltonian systems and optimal control
• KAM theory with applications to Hamiltonian partial differential equations
• Four lectures on KAM for the non-linear Schrödinger equation
• A Birkhoff normal form theorem for some semilinear PDEs
• Normal form of holomorphic dynamical systems
• Geometric approaches to the problem of instability in Hamiltonian systems. An informal presentation
• Variational methods for the problem of Arnold diffusion
• The calculus of variations and the forced pendulum
• Variational methods for Hamiltonian PDEs
• Spectral gaps of potentials in weighted Sobolev spaces
• On the well-posedness of the periodic KdV equation in high regularity classes.